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Portions not contributed by visitors are Copyright 2018 Tangient LLC
TES: The largest network of teachers in the world
Portions not contributed by visitors are Copyright 2018 Tangient LLC
TES: The largest network of teachers in the world
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Meantone is a familar historical temperament based on a chain of fifths (or fourths), which is discussed here in the context of the associated family of temperaments, and here in terms of 11-limit extensions.
History
Meantone was the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various Well Temperaments and eventually 12-tone Equal Temperament won in popularity.Theory and Classification
Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a rank-2 temperament. The octave is typically pure or close to pure, and the fifth is a few cents narrower than pure. The rationale for narrowing the fifth is to temper out the syntonic comma. This means that stacking four fifths (such as C-G-D-A-E) results in a major third (C-E) that is close to just.Intervals in meantone have standard names based on the number of steps of the diatonic scale they span (this corresponds to the val <7 11 16|), with a modifier {..."double diminished", "diminished", "minor", "major", "augmented", "double augmented"...} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.
Meantone Temperaments (ie, tunings)
Spectrum of Meantone Tunings by Eigenmonzos
Links